Multiple transmit and receive antennas may be used in multicarrier communication systems, such as multiple-input, multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems, to improve communication quality and capacity. OFDM effectively partitions the overall system bandwidth into a number of orthogonal frequency subchannels. These subchannels are also interchangeably referred to throughout this document as “tones” or “subcarriers.” Examples of such MIMO OFDM systems include, but are not limited to, WiMAX, IEEE 802.11a, IEEE 802.11g, IEEE 802.11n and 3GPP LTE. Such MIMO systems generally include a transmitter having multiple transmit antennas communicating with a receiver having one or more receive antennas (the number of transmit antennas and the number of receive antennas may or may not be equal). In a MIMO communication system, each of the transmit antennas transmits, at substantially the same time, M different symbols on the same group of subcarriers, where M is the number of transmit antennas. Although each transmit antenna transmits a respective symbol on at least some of the same subcarriers, the spacings between the antennas (e.g., approximately one half wavelength of the carrier frequency (for example, 5.4 GHz) that is modulated by the subcarriers) are selected so that the symbols may be recovered at the receiver. To generate the M symbols, a serial bit-stream may be converted into M groups of multi-bit subsymbols that each modulate a respective one of the subcarriers.
An accurate estimate of the signal response of the respective channel between each transmit antenna and each receive antenna is needed to effectively indicate which subcarriers are available for carrying subsymbols, and to effectively recover the symbols collectively transmitted on the available subcarriers. This channel estimation is typically performed by sending a group of predetermined training sequences from the transmitter (at least one predetermined sequence for each transmit antenna) and measuring the received training sequence at the receiver. Since the predetermined training sequences may have special orthogonal characteristics and are known a priori by the receiver, the respective signal response at each subcarrier for each channel may be estimated by correlating the received training sequences with the corresponding transmitted training sequences.